27 Feb 2013

Midweek Maths: A Purse Full of Ducats

Three men are sitting round a table. They each have some 1-ducat coins in front of them and there is a purse full of similar coins in the middle of the table.


Alessandro turns to Bruno and says:”If I add the ducats in the purse to my money I will have twice as many ducats as you.” Then Bruno turns to Cesare and says:”If I add the coins in the purse to my money, I will have three times as many ducats as you.” Finally, Cesare says to Alessandro:”If I add the ducats in the purse to those I already have, I will have four times as much money as you.”

How many ducats does each man have and how many are in the purse? Assume the smallest integer solution.

As in the previous question, Fibonacci did not use any algebra to solve this question. For students who feel that algebra is some kind of mental torture, try following a verbal algorithm nearly a page long!



Middle Secondary Level

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